三维齐次空间中的多谐曲面

Pub Date : 2023-11-13 DOI:10.1007/s00229-023-01520-4

S. Montaldo, C. Oniciuc, A. Ratto

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引用次数: 1

摘要

摘要本文第一部分对三维齐次空间(bianchi - cartan - vrancanu空间，简称bcv空间)中的固有三谐等参曲面进行了分类。我们还将证明三谐波霍普夫圆柱必然是CMC。在最后一节中，我们将确定bcv空间中CMC r -谐波Hopf圆柱的完整分类，$$r \ge 3$$ r≥3。这个结果保证了在合适的r值下，在bcv空间中存在大量的r -调和曲面的新实例。

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Polyharmonic surfaces in 3-dimensional homogeneous spaces

Abstract In the first part of this paper we shall classify proper triharmonic isoparametric surfaces in 3-dimensional homogeneous spaces (Bianchi-Cartan-Vranceanu spaces, shortly BCV-spaces). We shall also prove that triharmonic Hopf cylinders are necessarily CMC. In the last section we shall determine a complete classification of CMC r -harmonic Hopf cylinders in BCV-spaces, $$r \ge 3$$ r ≥ 3 . This result ensures the existence, for suitable values of r , of an ample family of new examples of r -harmonic surfaces in BCV-spaces.

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